reserve x,y for set,
  n,m for Nat,
  r,s for Real;

theorem Th13:
  for r be Real holds MIM(<*r*>) = <*r*>
proof
  let r be Real;
  set f = <*r*>;
A1: len f = 1 by FINSEQ_1:40;
  then
A2: len MIM(f) = 1 by Def2;
  then
A3: dom MIM(f) = Seg 1 by FINSEQ_1:def 3;
  now
    let n be Nat;
    assume n in dom MIM(f);
    then n = 1 by A3,FINSEQ_1:2,TARSKI:def 1;
    hence MIM(f).n = f.n by A1,A2,Def2;
  end;
  hence thesis by A1,A2,FINSEQ_2:9;
end;
